Related papers: Non-local homogenization limits of discrete elasti…
We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics…
To expand the framework available for interpreting experiments on disordered strongly correlated systems, and in particular to explore further the strong-coupling zero-bias anomaly found in the Anderson-Hubbard model, we ask how this…
We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long…
We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the…
We analyze Allen-Cahn functionals with stationary ergodic coefficients in the regime where the length scale $\delta$ of the heterogeneities is much smaller (microscopic) than the interface width $\epsilon$ (mesoscopic). In the main result,…
The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself…
We consider an abstract second order linear equation with a strong dissipation, namely a friction term which depends on a power of the "elastic" operator. In the homogeneous case, we investigate the phase spaces in which the initial value…
We find the free-energy in the thermodynamic limit of a one dimensional XY model associated to a system of N qubits. The coupling among the sigma_i^z is a long range two bodies random interaction. The randomness in the couplings is the…
In this work we consider the elasticity problem for two domains separated by a heterogeneous layer. The layer has an $\varepsilon-$periodic structure, $\varepsilon\ll1$, including a multiple micro-contact between the structural components.…
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective…
Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…
Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…
Local detailed balance (LDB) is a central guiding principle for modeling nonequilibrium stochastic dynamics, yet it only constrains the ratio of forward and backward transition rates and does not fix the steady state. Although the…
We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B {\bf 89}, 161306 (2014), Phys. Rev. B {\bf 93}, 115318 (2016)] have found, for a resonant electronic level…
We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…
We extend the duality of Kipnis Marchioro and Presutti to inhomogeneous lattice gas systems where either the components have different degrees of freedom or the rate of interaction depends on the spatial location. Then the dual process is…
We study non-linear adiabatic connection paths in density-functional theory using modified electron-electron interactions that perform a long-range/short-range separation of the Coulomb interaction. These adiabatic connections allows to…
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…